After having been on tumblr for who-knows-how-long (you lose track of time on that site, really) I've followed some awesome blogs where you can find a lot of DRRR stuff!
36-7This is a Durarara!! image blog. They post a lot of pictures, and always with the original source so you can go to the artist's page and see what else they've put up! They tag everything so it's easy to find something specific that you're looking for, whether it's a certain character or theme.
DRRR HeadcanonThis is a blog where people submit their own headcanons about the characters of Durarara!! (in case you don't know what a headcanon is, it's when you have a preconceived notion about the way a character talks, acts, thinks, lives, etc. that isn't explicitly canon but develops into your personal view of the character – for example, a headcanon I have about Shizuo is that he can cook).
Ikebukuro ConfessionsThis blog is where people confess things about Durarara!! that they might not talk about with other people. Be careful though — this one tends to get a lot of drama over shipping wars and people who can't stand other opinions. So keep an open mind when going to this blog!
Durarara Troll Secrets!This is like IkebukuroConfessions, except they're total crack and hilarious! Don't take this place seriously
at all! It's a beautiful blog if you want a good laugh.
Things DRRR Taught MeThingsDRRRTaughtMe is on Hiatus right now, but I'm sure they'll be back up soon! This blog, like the three above, is run by submissions from people who want to express something that they've learned from Durarara. It can be silly and it can be serious.
DRRR ScreencapsThis blog is a great place to find screencaps from the anime that you may want to use for icons, graphics, etc!
That's it for now! I'll post more here when I remember them, and others can post too if they know of any great Durarara-related tumblrs~